Point Slope Equation of a Line
Point Slope Equation of a Line
Any time you are given the slope of a line (m)
and a point on the line ( x1, y1 )
Use the point-slope equation of a line to solve.
y – y1 = m ( x – x1 )
Point Slope Equation of a Line
m = 5; ( 2, 3 )
Use the point-slope equation of a line to solve.
y – y1 = m ( x – x1 )
y–3=5(x–2)
Slope-intercept Equation of a Line
y–3=5(x–2)
y – 3 = 5x – 10
y = 5x – 7
This is the slope-intercept equation of the line
with a slope of 5 passing through the point ( 2, 3 )
Standard Equation of a Line
y = 5x – 7
This is the slope-intercept equation of the line
with a slope of 5 passing through the point ( 2, 3 )
If they want the answer in standard form
Ax + By = C
just rearrange the furniture!
- 5x + y = -7
A matter of style
- 5x + y = -7
Some textbook authors dislike starting with a negative.
Although this is a correct answer, if it is not included in the
multiple choice answers, clean it up by multiplying everything
by -1.
5x – y = 7
Oh no! A Fraction!
What if the slope is a fraction?
M = 2/3 ; ( - 7, - 5 )
We still use
y – y1 = m ( x – x1 )
2
y  (5)  [ x  (7)]
3
Oh no! A Fraction!
y – y1 = m ( x – x1 )
2
y  (5)  [ x  (7)]
3
Notice how I use parentheses to keep my signs straight!
Clean up the double signs
2
y  (5)  [ x  (7)]
3
2
y  5  [ x  7]
3
Fractions and Equal Signs
2
y  5  [ x  7]
3
Whenever you have a fraction and an equal sign,
multiply both sides of the equation by the LCD.
Fractions and Equal Signs
2
y  5  [ x  7]
3
2
3( y  5)  3( )[ x  7]
3
3 y  15  2 x  14
Finish Up!
3 y  15  2 x  14
3 y  2x 1
2
1
y  x
3
3
Answer in slope-intercept form
Finish Up!
3 y  2x 1
2 x  3 y  1
2x  3y  1
Answer in standard form with no leading negative.
Point- slope equation of a line
1. If you know a point ( x1, y1 ) and the slope m.
2. Use y – y1 = m ( x – x1 )
3. Distribute the m
4. Move the y1
5. This gives the slope-intercept equation of the line.
6. If they want it in standard form, rearrange the
furniture ( and you may have to clear a leading
negative).